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I've played Pokemon on an old 3DS XL, regular N3DS, and a N3DS XL.
The new 3DS models have much more efficient processors. They start up games faster and download games faster as well.
As far as Pokemon goes, the 3D feature is still laggy on both old and new models.
Graphically, they're almost identical. The text is sharper on the smaller models, whereas it can look a bit fuzzy on the XL ones. However, when you're actually battling the graphics are pretty much the same on the small and XL versions.
I recommend the N3DS XL because the larger screen is very luxurious and provides a more immersive gaming experience. It's faster and has a longer battery life.
That being said though, it's not a huge leap from the old 3DS XL. But if you're moving from an old regular 3DS or a 2DS, then the upgrade is definitely worth it.
When it comes to Pokemon, there aren't much differences. These differences are more pronounced when you play a game like Smash Bros or Monster Hunter.